Assignment

Question 1: A drum of 50 cm radius is rolling along the ground at a speed of 8.5 m/s.

a) What is the rotational speed of the cylinder about its axis?

b) What is the magnitude and direction of acceleration of a point on the drum's surface?

c) At the instant when the certain point on the drum's surface is at the top of the drum, what is the velocity of the point?

d) At the instant when the certain point on the drum's surface is at the top of the drum, what is the velocity of the point?

Question 2: Two thin hoops with masses m₁ and m₂ with radii r₁ and r₂ are mounted rigidly on a frame of negligible mass. Find the moment of inertia of the system about an axis perpendicular to the page and through the centre of the hoops.

Question 3: The lower (orange) disk is coasting with angular speed ω₁. The combined moment of inertia of the disk and the axle is I₁. A second disk (grey) with moment of inertia I₂ is dropped onto the first disk and rotates with the first disk. Find the angular velocity of the combined disks when the original angular velocity of the grey disk was:

a) ω₂ = 0

b) ω₂ = 2ω₁ and is in the same direction as ω₁

c) ω₂ = 1.2ω₁ and is in the opposite direction as ω₁

Question4: The equation of motion of a simple pendulum is given by:

θ = 18sin(2.5πt + 0.45)

Find the: a) amplitude, b) frequency, c) period d) phase change in degrees and e) length, L of the pendulum.

Question 5: A 0.45 m long string oscillates in five segments when a frequency of 250 Hz is used to drive it. What is the: a) wavelength, b) speed of the wave, c) what frequency will cause the string to vibrate in the fundamental harmonic?

Question 6: A police car chases a speeding car along a straight road. Both vehicles move at 120 km/hr. The police car siren has a frequency of 510 Hz. What is the Doppler shift in the frequency heard by the speeding car?

Question 7: The shear modulus for a metal is 5.5 x 10¹⁰ Nm^-2. A shear force of 250 N is applied to the upper surface of a cube of this metal. The cube measures 5cm along each edge. How far will the top surface be displaced?

Question 8: The pipe near the lower end of a large water storage tank springs a small leak, and a stream of water shoots out. If the top of the water in the tank is 15 m above the leak, at what speed does the stream of water travel out of the hole? If the hole has an area of 1.5 x 10^-6m^-2, how much water flows out in 5 s?

Question 9: The density of ice is 917 kgm^-3 and the approximate density of the seawater in which an iceberg floats is 1050 kgm^-3. What fraction of the iceberg is beneath the surface of the water?

Question 10: A small glass sphere has a radius of 0.25 mm and a density of 2500 kgm^-3. The sphere is dropped in a vat of oil (ρ = 920 kgm^-3, η = 0.23 PI). Find a) the buoyant force on the sphere, b) the gravitational force on the sphere, c) use Stokes law to find the terminal speed of the sphere as it falls through the oil.

Question11: A uniform solid brass sphere of radius, r, and mass, m, is set spinning with angular speed ω about an axis through the diameter of the sphere. If the temperature is increased from room temperature, 25^oC, to 95^oC without disturbing the sphere, determine a) the angular speed and b) the rotational kinetic energy at 95^oC.